SYMPLECTIC CONNECTIONS AND THE LINEARIZATION OF HAMILTONIAN-SYSTEMS

被引:30
作者
MARSDEN, JE
RATIU, T
RAUGEL, G
机构
[1] CORNELL UNIV,ITHACA,NY 14853
[2] UNIV CALIF SANTA CRUZ,DEPT MATH,SANTA CRUZ,CA 95064
[3] MATH SCI RES INST,BERKELEY,CA 94720
[4] UNIV PARIS 11,CNRS,ANAL NUMER LAB,UA D760,F-91405 ORSAY,FRANCE
基金
美国国家科学基金会;
关键词
D O I
10.1017/S030821050002477X
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper uses symplectic connections to give a Hamiltonian structure to the first variation equation for a Hamiltonian system along a given dynamic solution. This structure generalises that at an equilibrium solution obtained by restricting the symplectic structure to that point and using the quadratic form associated with the second variation of the Hamiltonian (plus Casimir) as energy. This structure is different from the well-known and elementary tangent space construction. Our results are applied to systems with symmetry and to Lie-Poisson systems in particular.
引用
收藏
页码:329 / 380
页数:52
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